exterior angle

简明释义

外角

英英释义

例句

1.Understanding the properties of the exterior angle 外角 is crucial for solving complex geometric problems.

理解外角外角的性质对于解决复杂的几何问题至关重要。

2.To solve the problem, we need to calculate the exterior angle 外角 of the given shape.

要解决这个问题，我们需要计算给定形状的外角外角。

3.The measure of the exterior angle 外角 of a triangle is equal to the sum of the two opposite interior angles.

三角形的外角外角的度数等于两个对边内角的和。

4.In geometry, the exterior angle 外角 theorem helps us find unknown angles in polygons.

在几何中，外角外角定理帮助我们找到多边形中未知的角。

5.The exterior angle 外角 at each vertex of a regular pentagon measures 72 degrees.

正五边形每个顶点的外角外角为72度。

作文

In geometry, an exterior angle is formed when one side of a polygon is extended outwards. The angle that is created between this extended side and the adjacent side of the polygon is known as the exterior angle. Understanding exterior angles is crucial in various fields, including architecture, engineering, and even art. This concept is not only fundamental in theoretical mathematics but also has practical applications in real-world scenarios.To illustrate the importance of exterior angles, let's consider a simple triangle. When one side of the triangle is extended, the angle formed outside the triangle is its exterior angle. According to the properties of triangles, the sum of the exterior angles of any polygon is always equal to 360 degrees. This property holds true regardless of the number of sides the polygon has. For example, if we have a triangle with angles measuring 60, 70, and 50 degrees, extending one of its sides will yield an exterior angle of 120 degrees. This relationship helps us verify our calculations and understand the geometric properties of shapes more deeply.The significance of exterior angles extends beyond just triangles. In polygons with more sides, such as quadrilaterals or pentagons, the same principle applies. For instance, in a rectangle, each corner has an exterior angle of 90 degrees when extended. Therefore, the total exterior angles for a rectangle would also add up to 360 degrees. This consistency across different shapes highlights the beauty and symmetry present in geometry.Moreover, exterior angles play a vital role in solving problems related to angles and measurements. For example, architects use these principles when designing buildings, ensuring that structures are stable and aesthetically pleasing. Engineers also apply these concepts in their work, particularly when creating blueprints or models that require precise angle measurements. Artists may utilize exterior angles in their compositions to create visual balance and harmony.In addition to practical applications, understanding exterior angles can enhance our problem-solving skills. When faced with complex geometric problems, recognizing the relationships between exterior angles and their corresponding interior angles can simplify the process. It allows students and professionals alike to approach problems from different angles, literally and figuratively.In conclusion, the concept of exterior angles is a fundamental aspect of geometry that has far-reaching implications. Whether in mathematics, architecture, engineering, or art, the understanding of exterior angles enriches our comprehension of shapes and their properties. As we continue to explore and apply these concepts, we gain not only mathematical skills but also a deeper appreciation for the world around us. Thus, mastering the idea of exterior angles is essential for anyone looking to excel in fields that rely on geometry.

在几何学中，外角是指当多边形的一条边向外延伸时形成的角。这个延伸边与多边形的邻接边之间形成的角被称为外角。理解外角在建筑、工程甚至艺术等多个领域至关重要。这个概念不仅在理论数学中是基础，而且在现实世界的各种场景中也有实际应用。为了说明外角的重要性，让我们考虑一个简单的三角形。当三角形的一条边被延伸时，三角形外部形成的角就是它的外角。根据三角形的性质，任何多边形的外角之和总是等于360度。这一性质适用于多边形的边数。例如，如果我们有一个角分别为60、70和50度的三角形，延伸其中一条边将产生一个外角为120度。这个关系帮助我们验证计算并更深入地理解形状的几何特性。外角的重要性不仅限于三角形。在更多边的多边形中，例如四边形或五边形，同样的原则适用。例如，在矩形中，每个角在延伸时都有一个外角为90度。因此，矩形的总外角也将加起来等于360度。这种在不同形状中的一致性突显了几何学的美与对称。此外，外角在解决与角度和测量相关的问题中发挥着重要作用。例如，建筑师在设计建筑时会使用这些原理，以确保结构稳定且美观。工程师在制作需要精确角度测量的蓝图或模型时也应用这些概念。艺术家可能在他们的作品中利用外角来创造视觉平衡和和谐。除了实际应用，理解外角可以增强我们的解决问题的能力。当面对复杂的几何问题时，识别外角与其对应的内角之间的关系可以简化过程。这使得学生和专业人士能够从不同的角度（字面和比喻上）来处理问题。总之，外角的概念是几何学的一个基本方面，具有广泛的影响。不论是在数学、建筑、工程还是艺术中，理解外角丰富了我们对形状及其属性的理解。随着我们继续探索和应用这些概念，我们不仅获得了数学技能，还对周围的世界有了更深的欣赏。因此，掌握外角的概念对于任何希望在依赖几何的领域中脱颖而出的人来说都是必不可少的。